Question

等差数列an的前n项和为Sn,且S5=45,S6=60?①求an的通项公式an?②若数列an满足bn+1-bn＝an(n

Answer 1

①S5=45,S6=60

a6=S6-S5=15

S6=(a1+a6)*3

a1=5,d=2,an=2n+3

②bn+1-bn＝an=2n+3

b2-b1=5

b3-b2=7

...

bn-bn-1=2n+1,叠加法

bn=n^2+2n,1/bn=1/n(n+2)=(1/2)[(1/n)-(1/n+2)

然后就能算Tn了